Annual average energy of load profiles

In this analysis, the average load profiles of the synthetic and measured customers are compared with type consumer load profiles. In this thesis, synthetic load profiles are generated using the input data set measured in 2016. That data set is fed directly into the input of the synthetic load profile generator without any composing of data such as temperature normalization. The output of the synthetic load profile generator is based on the measured data. Therefore, the output of the synthetic load profile generator also can be thought of as a load profile without temperature normalization. However, the type consumer load profiles provided in the study material are temperature normalized and applied to 2018 calendar. Therefore, in order to compare average measured customer or synthetic average load profiles with the type consumer load profiles, first, those aver-age load profiles must be temperature normalized and then projected from 2016 to 2018.

Figure 6.3 shows the flow chart of the average profile forming procedure developed to compare with the type consumer load profiles.

The flow chart shown in Figure 6.3 is applied to a chosen type consumer class and this average profile forming procedure was implemented in MATLAB. The function starts with loading the load profiles (i.e. measured or synthetic load profiles in 2016) to the program, then generating the average load profile for the given input load profiles. After that, the temperature dependency parameters are fetched for the type consumer class of the in-put load profiles from the study material, and the average load profile is temperature normalized using the method explained in subchapter 5.7. The temperature normaliza-tion allows consumpnormaliza-tion data to be treated equally to other years. Later, the temperature normalized average load profile should be projected to 2018 in order to change the week-days and special week-days of 2016 to corresponding week-days of 2018. Antti Mutanen has devel-oped a function in his research for projecting load profiles between years. In this thesis, the same function has been used to project the temperature normalized load profiles from 2016 to 2018. After applying this process, this temperature normalized and pro-jected average load profile can be used to compare with the corresponding type con-sumer load profile in the study material. Rest of the content in this subchapter uses the term average load profile for temperature normalized and projected average load profile.

There are 14 type consumer classes in the study material, and synthetic, measured av-erage load profiles for type consumer classes 1, 4, 7 and 10 are shown in Figure 6.4.

The first and second columns represent the synthetic and measured average load pro-files respectively, while the third column represents the corresponding type consumer load profile from the study material.

Figure 6.3 Flow chart of the average profile forming procedure in order to compare the average load profile with given type consumer class load profiles in the study material

Figure 6.4 Average load profiles for type consumer classes 1,4,7 and 10 (rows 1,2,3,4 re-spectively); Columns represents (a) average profile from 100 generated synthetic load profiles

(b) from measured customer load profiles (c) type consumer load profile.

Consumer Type 1

(a) (b) (c)

Consumer Type 4

(a) (b) (c)

Consumer Type 7

(a) (b) (c)

Consumer Type 10

(a) (b) (c)

According to Figure 6.4, the synthetic average load profile of each type consumer class has followed the shape of its corresponding measured customer average load profile almost identically. At first glance, synthetic and measured average load profiles look very similar, because the highlighted spikes and variations look also similar in both load pro-files. This is quite natural because the measured data set is the input for synthetic load profile generator. Both these average load profiles are less smooth with compared to its corresponding type consumer load profile. The type consumer load profile is derived for comparatively a large number of customers (i.e. from the large data set), therefore, the spikes have been eliminated. However, the measured data set is a small data set com-pared to the large data set, and this might be the reason for having less smoothness in the measured average load profile. Therefore, the synthetic load profiles appear to be trying to follow the measured data set. However, the sample size is only 100, so that it is too early to guess without testing this for a large sample of synthetic load profiles. This will be analyzed for a large sample of synthetic load profiles in subchapter 6.3.

The annual average energy for each type consumer class was calculated from the de-rived synthetic and measured average load profiles. Average annual energies for type consumer classes are already available in the study material. All these values are illus-trated in Table 6.2. Table 6.2 also includes the calculated average energies of average load profiles with and without temperature normalization. The absolute percentage errors of the annual average energy values between the measured and synthetic average load profiles as well as type consumer load profile and synthetic average load profile were also calculated and tabulated in Table 6.3 for each type consumer class. As can be seen from the tables, there are slight differences between the annual average energy values.

Table 6.3 shows that the error between measured and synthetic average load profiles ranges from 0.20 % to 4.08 % for type consumer classes 1-12. But in the same column, type consumer classes 13 and 14 have comparatively bit higher errors (i.e. 9.29 % and 6.78 % respectively) than others. However, these high errors are still less than 10% and moderately acceptable. The annual average energy error between type consumer and synthetic load profiles are comparatively higher than the errors between measured and synthetic average load profiles.

Table 6.2 Average annual energies calculated for type consumer load profiles and, synthetic and measured load profiles with and without temperature normalization

Table 6.3 Percentage errors between annual average energy values of synthetic and meas-ured average load profiles/ synthetic average and type consumer load profiles

Type

consumer Annual average energy error (%) between synthetic

As shown in Table 6.2, the average annual energies of synthetic and measured custom-ers in type consumer class 13 and 14 are significantly lower than their corresponding type consumer load profile’s average annual energy compared to other type consumer classes. The reason for that is, the type consumer classes 13 and 14 consist only 21 and 7 customers respectively in the measured data set, and their power consumption values are also typically high. The type consumer classes 13 and 14 refer industrial customers connected to medium voltage network with 1 shift and 3 shifts respectively. The load behaviour of different customers in these classes can be numerous. Therefore, such a small number of customers in a type consumer class with high power consumers may not reflect the large data set. Therefore, repeating the fact that the annual average en-ergy errors in type consumer classes 13 and 14 are relatively high in both columns in Table 6.3 compared to the others. Furthermore, it is known that the measured data set used to derive the average load profiles is small data set compared to the large data set.

So, the average energy values from the measured data set are more sensitive and can fluctuate for load changes. Due to these reasons and according to the conclusion from the comparison of the tables, average annual energies of measured and synthetic aver-age load profiles tend to each other because MC follows the input data set, while the errors between synthetic and type consumer load profiles are comparatively high always.

Another significant big error that could be observed in the 2nd column is 12.10 % for type consumer class 1. The customers in type consumer class 1 consume less hourly power throughout the year (e.g. most of the hourly powers are less than 1 kW in the time series), so the percentage error equation yields a high error due to its ratio.

Table 6.4 represents the calculated MAPEs for the same above mentioned synthetic average load profiles against measured average and type consumer load profiles to measure the accuracy of the synthetic average load profiles data. As seen from Table 6.4, the MAPEs between the type consumer and synthetic average load profiles plus the type consumer and measured average load profiles are both considerably higher and approximately close each other. But the MAPEs between measured and synthetic aver-age load profiles are comparatively very low. Therefore, there is a relatively balanced data flow between measured and synthetic average load profile data sets. Also, for the type consumer class 1, a significant higher MAPE can be observed in all three columns of Table 6.4. Based on the MAPE equation, if actual values are too small (e.g. less than 1), the ratio becomes a more substantial value, and eventually, the outcome returns a large error percentage. In the type consumer class 1, the power values are comparatively low and there is a large percentage of data with less than 1kW power consumption val-ues. Due to this reason, MAPEs of the type consumer class 1 are considerably higher.

Table 6.4 Calculated MAPEs for the synthetic average load profiles against measured average and type consumer class load profiles